Abstract
Manipulation of non-Markovian dynamics of open quantum systems has become an important topic in the field of quantum information since quantum non-Markovianity has been proved to be a potential quantum resource. Here, focusing on a simple yet well-known model of a two-level system coupled to bosonic fields, we study how to control the non-Markovian dynamics of an open quantum system using quantum-jump-based feedback control. Numerical simulations show that the quantum-jump-based feedback control can be used to enhance the measure of non-Markovianity. We find that the non-Markovianity can further be optimized by choosing appropriate feedback amplitude. These results may trigger potential applications in exploring non-Markovian effect for future quantum technology and quantum memory.
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Breuer, H.P., Petruccione, F.: The Theory of Open Quantum Systems. Oxford University Press, Oxford (2001)
Zhang, D.J., Huang, H.L., Tong, D.M.: Non-Markovian quantum dissipative processes with the same positive features as Markovian dissipative processes. Phys. Rev. A 93(1–5), 012117 (2016)
Zhang, D.J., Yu, X.-D., Huang, H.-L., Tong, D.M.: General approach to find steady-state manifolds in Markovian and non-Markovian systems. Phys. Rev. A 94(1–8), 052132 (2016)
Chin, A.W., Huelga, S.F., Plenio, M.B.: Quantum metrology in non-Markovian environments. Phys. Rev. Lett. 109(1–5), 233601 (2012)
Bai, K., Peng, Z., Luo, H.-G., An, J.-H.: Retrieving ideal precision in noisy quantum optical metrology. Phys. Rev. Lett. 123(1–6), 040402 (2019)
Vasile, R., Olivares, S., Paris, M.G.A., Maniscalco, S.: Continuous-variable quantum key distribution in non-Markovian channels. Phys. Rev. A 83(1–6), 042321 (2011)
Davies, E.B.: Quantum Theory of Open Systems. Academic Press, Cambridge (1976)
Xu, K., Han, W., Zhang, Y.-J., Xia, Y.-J., Fan, H.: Hierarchical-environment-assisted non-Markovian speedup dynamics control. Phys. Rev. A 98(1–7), 022114 (2018)
Aolita, L., De Melo, F., Davidovich, L.: Open-system dynamics of entanglement: a key issues review. Rep. Prog. Phys 78(1–79), 042001 (2015)
Franco, R.L., Bellomo, B., Maniscalco, S., Compagno, G.: Dynamics of quantum correlations in two-qubit systems within non-Markovian environments. Int. J. Mod. Phys. B 27(1–20), 1345053 (2013)
Xu, J.-S., Sun, K., Li, C.-F., Xu, X.-Y., Guo, G.-C., Andersson, E., Franco, R.L., Compagno, G.: Experimental recovery of quantum correlations in absence of system-environment back-action. Nat. Commun. 4(1–7), 2851 (2013)
Orieux, A., D’Arrigo, A., Ferranti, G., Franco, R.L., Benenti, G., Paladino, E., Falci, G., Sciarrino, F., Mataloni, P.: Experimental on-demand recovery of quantum entanglement by local operations within non-Markovian dynamics. Sci. Rep. 5(1–8), 8575 (2015)
D’Arrigo, A., Franco, R.L., Benenti, G., Paladino, E., Falci, G.: Recovering entanglement by local operations. Ann. Phys. 350, 211–224 (2014)
Man, Z.-X., Xia, Y.-J., Franco, R.L.: Cavity-based architecture to preserve quantum coherence and entanglement. Sci. Rep. 5(1–13), 13843 (2015)
Mortezapour, A., Naeimi, G., Franco, R.L.: Coherence and entanglement dynamics of vibrating qubits. Optics. Commun. 424, 26–31 (2018)
Mirkin, N., Poggi, P., Wisniacki, D.: Entangling protocols due to non-Markovian dynamics. Phys. Rev. A 99(1–5), 020301 (2019)
Mortezapour, A., Borji, M.A., Franco, R.L.: Protecting entanglement by adjusting the velocities of moving qubits inside non-Markovian environments. Laser. Phys. Lett. 14(1–9), 055201 (2017)
Franco, R.L., D’Arrigo, A., Falci, G., Compagno, G., Paladino, E.: Preserving entanglement and nonlocality in solid-state qubits by dynamical decoupling. Phys. Rev. B 90(1–11), 054304 (2014)
Dijkstra, A.G., Tanimura, Y.: Non-Markovian entanglement dynamics in the presence of system-bath coherence. Phys. Rev. Lett. 104(1–4), 250401 (2010)
Mortezapour, A., Franco, R.L.: Protecting quantum resources via frequency modulation of qubits in leaky cavities. Sci. Rep. 8(1–17), 14304 (2018)
Man, Z.-X., An, N.B., Xia, Y.-J.: Non-Markovian dynamics of a two-level system in the presence of hierarchical environments. Optics. Exp. 23(1–14), 5763 (2015)
Breuer, H.P., Laine, E.M., Piilo, J.: Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems. Phys. Rev. Lett. 103(1–4), 210401 (2009)
Rivas, A., Huelga, S.F., Plenio, M.B.: Entanglement and non-Markovianity of quantum evolutions. Phys. Rev. Lett. 105(1–4), 050403 (2010)
Wolf, M.M., Cirac, J.I.: Dividing quantum channels. Commun. Math. Phys. 279, 147–168 (2008)
Breuer, H.P., Laine, E.M., Piilo, J., Vacchini, B.: Colloquium: non-markovian dynamics in open quantum systems. Rev. Mod. Phys. 88(1–24), 021002 (2016)
Lu, X.-M., Wang, X., Sun, C.P.: Quantum Fisher information flow and non-Markovian processes of open systems. Phys. Rev. A 82(1–4), 042103 (2010)
Luo, S., Fu, S., Song, H.: Quantifying non-Markovianity via correlations. Phys. Rev. A 86(1–4), 044101 (2012)
Bylicka, B., Chruscinski, D., Maniscalco, S.: Non-Markovianity and reservoir memory of quantum channels: a quantum information theory perspective. Sci. Rep. 4(1–7), 5720 (2014)
Fanchini, F.F., Karpat, G., Cakmak, B., Castelano, L.K., Aguilar, G.H., Farias, O.J., Walborn, S.P., Ribeiro, P.H.S., de Oliveira, M.C.: Non-Markovianity through Accessible Information. Phys. Rev. Lett 112(1–6), 210402 (2014)
He, Z., Yao, C., Wang, Q., Zou, J.: Measuring non-Markovianity based on local quantum uncertainty. Phys. Rev. A 90(1–7), 042101 (2014)
Dhar, H.S., Bera, M.N., Adesso, G.: Characterizing non-Markovianity via quantum interferometric power. Phys. Rev. A 91(1–9), 032115 (2015)
Liu, B.-H., Li, L., Huang, Y.-F., Li, C.-F., Guo, G.-C., Laine, E.M., Breuer, H.P., Piilo, J.: Experimental control of the transition from Markovian to non-Markovian dynamics of open quantum systems. Nature Physics. 7, 931–934 (2011)
Apollaro, T.J.G., Franco, C.D., Plastina, F., Paternostro, M.: Memory-keeping effects and forgetfulness in the dynamics of a qubit coupled to a spin chain. Phys. Rev. A 83(1–10), 032103 (2011)
Brito, F., Werlang, T.: A knob for Markovianity. New. J. Phys. 17(1–9), 072001 (2015)
Lorenzo, S., Plastina, F., Paternostro, M.: Tuning non-Markovianity by spin-dynamics control. Phys. Rev. A 87(1–7), 022317 (2013)
Addis, C., Ciccarello, F., Cascio, M., Palma, G.M., Maniscalco, S.: Dynamical decoupling efficiency versus quantum non-Markovianity. New. J. Phys. 17(1–11), 123004 (2015)
Pang, S., Brun, T.A., Jordan, A.N.: Abrupt transitions between Markovian and non-Markovian dynamics in open quantum systems. arXiv:1712.10109 (2017)
Wang, J., Wiseman, H.M., Milburn, G.J.: Dynamical creation of entanglement by homodyne-mediated feedback. Phys. Rev. A 71(1–9), 042309 (2005)
Carvalho, A.R.R., Hope, J.J.: Stabilizing entanglement by quantum-jump-based feedback. Phys. Rev. A 76(1–4), 010301 (2007)
Hou, S.C., Huang, X.L., Yi, X.X.: Suppressing decoherence and improving entanglement by quantum-jump-based feedback control in two-level systems. Phys. Rev. A 82(1–6), 012336 (2010)
Wiseman, H.M.: Quantum theory of continuous feedback. Phys. Rev. A 49, 2133–2150 (1994)
Breuer, H.P.: Foundations and measures of quantum non-Markovianity. J. Phys. B. 45(1–12), 154001 (2012)
Laine, E.M., Piilo, J., Breuer, H.P.: Measure for the non-Markovianity of quantum processes. Phys. Rev. A 81(1–8), 062115 (2010)
Wißmann, S., Karlsson, A., Laine, E.M., Piilo, J., Breuer, H.P.: Optimal state pairs for non-Markovian quantum dynamics. Phys. Rev. A 86(1–6), 062108 (2012)
Streltsov, A., Adesso, G., Plenio, M.B.: Colloquium: quantum coherence as a resource. Rev. Mod. Phys 89(1–34), 041003 (2017)
Hu, M.-L., Hu, X., Wang, J.-C., Peng, Y., Zhang, Y.-R., Fan, H.: Quantum coherence and geometric quantum discord. Phys. Rep. 762–764, 1–100 (2018)
Zhang, D.J., Liu, C.L., Yu, X.D., Tong, D.M.: Estimating coherence measures from limited experimental data available. Phys. Rev. Lett. 120(1–6), 170501 (2018)
Myatt, C.J., King, B.E., Turchette, Q.A., Sackett, C.A., Kielpinski, D., Itano, W.M., Monroe, C., Wineland, D.J.: Decoherence of quantum superpositions through coupling to engineered reservoirs. Nature 403, 269–273 (2000)
Piilo, J., Maniscalco, S.: Driven harmonic oscillator as a quantum simulator for open system. Phys. Rev. A 74(1–11), 032303 (2006)
Acknowledgements
This work was supported by NSF-China under Grant Nos. 11904071, 11374085, the Key Program of the Education Department of Anhui Province under Grant Nos. KJ2017A922, KJ2019A0725, the Anhui Provincial Natural Science Foundation under Grant Nos. 1908085QA40, 1708085MA12, 1708085MA10, the discipline top-notch talents Foundation of Anhui Provincial Universities under Grants Nos.gxbjZD2017024, gxbjZD2016078, the Anhui Provincial Candidates for academic and technical leaders Foundation under Grant No. 2019H208.
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Zong, XL., Song, W., Yang, M. et al. Enhancing non-Markovianity by quantum feedback control. Quantum Inf Process 19, 131 (2020). https://doi.org/10.1007/s11128-020-02629-1
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DOI: https://doi.org/10.1007/s11128-020-02629-1